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For example, when someone talks about the "post to post" elevation error of a DTM, what exactly are they referring to?

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Post means simply an elevation point. You can find a definition for example from the GDIWG standard https://portal.dgiwg.org/files/?artifact_id=11998&format=pdf

post The locations of the intersections of rows and columns within an elevation grid. Post spacing for a rectified grid is a measure of its horizontal resolution

The circles in this image are posts. Notice that the posts are at the intersection of the elevation grid and the rectangles in the image are not pixels. Typically a post is located at the centre of a pixel if DEM is stored as GeoTIFF.

enter image description here

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    Whilst this is the correct answer, I'm also thinking it's a linguistic hangover from surveying. The posts are survey posts.
    – Andrew Tice
    Commented May 23 at 7:06

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